transmission

transmission(from::Int, arr1::AbstractMatrix{T}, arr2::AbstractMatrix{T}, q::Q; method = :BOmega) where {T}

Given a transmission condition q, calculate the transmission effect using the either the :BOmega method (the default), or the :irfs method.

Arguments

from::Int: Shock number.
arr1::AbstractMatrix{T}. In case of :BOmega this must be B, in case of :irfs this must be irfs. See the documentation for the specific methods for transmission(..., ::Type{Val{:BOmega}}) and transmission(...,::Type{Val{:irfs}}).
arr2::AbstractMatrix{T}: In case of :BOmega this must be Omega, in case of :irfs this must be irfs_ortho. See the documentation for the specific methods for transmission(..., ::Type{Val{:BOmega}}) and transmission(...,::Type{Val{:irfs}}).
q::Q: A transmission condition. See also Q.

Keyword Arguments

method::Symbol: Either :BOmega in which case the transmission effect will be calculated using the second method in Wegner et al (2024), or :irfs in which case the transmission effect is calculated using the first method in Wegner et al (2024).

Returns

Returns a Vector{T} with entry i corresponding to the transmission effect on variable \(x_i\). If \(x_k\) is the variable in the transmission condition with the highest subscript, then all entries in the returned vector with index less thatn k are NaN since interpretation of those results is nonsensical.

Exa```{julia}es

k = 6
h = 3
s = "(x1 | x2) & !x3"
cond = make_condition(s)

B = randn(k*(h+1), k*(h+1))
Omega = randn(k*(h+1), k*(h+1))

effect = transmission(1, B, Omega, cond; method = :BOmega)
effect = transmission(1, B, Omega, cond)  # same as above; default is :BOmega

irfs = randn(k, k, h+1)
irfs_ortho = randn(k, k, h+1)

irfs = to_transmission_irfs(irfs)
irfs_ortho = to_transmission_irfs(irfs_ortho)

effect = transmission(1, irfs, irfs_ortho, cond; method = :irfs)

transmission

transmission(
    from::Int, 
    B::AbstractMatrix{T},
    Omega::AbstractMatrix{T}, 
    q::Q, 
    ::Type{Val{:BOmega}}
) where {T}

Given a transmission condition q, calculate the transmission effect using the :BOmega method.

Arguments

from::Int: Shock number.
B::AbstractMatrix{T}: Part of the systems representation in Wegner et al (2024).
Omega::AbstractMatrix{T}: Part of the systems representation in Wegner et al (2024).
q::Q: A transmission condition. See also Q.

Returns

Returns a Vector{T} with entry i corresponding to the transmission effect on variable \(x_i\). If \(x_k\) is the variable in the transmission condition with the highest subscript, then all entries in the returned vector with index less thatn k are NaN since interpretation of those results is nonsensical.

Exa```{julia}es

k = 6
h = 3
s = "(x1 | x2) & !x3"
cond = make_condition(s)

B = randn(k*(h+1), k*(h+1))
Omega = randn(k*(h+1), k*(h+1))

effect = transmission(1, B, Omega, cond)

transmission

transmission(from::Int, 
    irfs::AbstractMatrix{T}, 
    irfs_ortho::AbstractMatrix{T}, 
    q::Q, 
    ::Type{Val{:irfs}}
) where {T}

Given a transmission condition q, calculate the transmission effect using the :irfs method.

Arguments

from::Int: Shock number.
irfs::AbstractMatrix{T}: Impulse responses. These should be in the form of the structural transmission model. See also to_transmission_irfs.
irfs_ortho::AbstractMatrix{T}: Orthogonalised IRFs. These should be in the form of the structural transmission model. See also to_transmission_irfs.
q::Q: A transmission condition. See also Q.

Returns

Returns a Vector{T} with entry i corresponding to the transmission effect on variable \(x_i\). If \(x_k\) is the variable in the transmission condition with the highest subscript, then all entries in the returned vector with index less thatn k are NaN since interpretation of those results is nonsensical.

Exa```{julia}es

k = 6
h = 3
s = "(x1 | x2) & !x3"
cond = make_condition(s)

irfs = randn(k, k, h+1)
irfs_ortho = randn(k, k, h+1)

irfs = to_transmission_irfs(irfs)
irfs_ortho = to_transmission_irfs(irfs_ortho)

effect = transmission(1, irfs, irfs_ortho, cond; method = :irfs)

transmission

transmission(model::Model, 
             from::Int, 
             q::Q, 
             order::AbstractVector{<:Int}, 
             max_horizon::Int) --> Array{<:Number, 3}

transmission(model::Model, 
             method::AbstractIdentificationMethod, 
             from::Int, 
             q::Q,
             order::AbstractVector{<:Int}, 
             max_horizon::Int) --> Array{<:Number, 3}

transmission(model::Model, 
             from::Int, 
             q::Q, 
             order::AbstractVector{Symbol}, 
             max_horizon::Int) --> Array{<:Number, 3}

transmission(model::Model, 
             method::AbstractIdentificationMethod, 
             from::Int, 
             q::Q,
             order::AbstractVector{Symbol}, 
             max_horizon::Int) --> Array{<:Number, 3}

Compute the transmission effect of a transmission channel defined by the condition q. If model is a reduced-form model, method will be used to identify the required structural shock.

Arguments

model::Model: A model, such as an SVAR, VAR, or LP.
method::AbstractIdentificationMethod: An identification method to identify the from-th structural shock.
from::Int: Shock number.
q::Q: A transmission condition. See also Q and make_condition.
order::AbnstractVector{<:Int}: order of variables defined by the transmission matrix using variable indices.
order::AbnstractVector{Symbol}: order of variables defined by the transmission matrix using variable names.
max_horizon::Int: Maximum horizon for the transmission effect.

Returns

Returns a three dimensional array with the first dimension correspondin to the endogenous variables (in original order), the second to the shock, and the third to the horizon (from 0 to max_horizon).